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Forum: Prime Gap Searches 2022-05-17, 17:22
Replies: 46
Views: 10,646
Posted By mart_r
I've only recently noted the changes to A048670....

I've only recently noted the changes to A048670. It's up to the 64th prime (311) now.

Why does nobody keep me in the loop?:no:
Forum: Prime Gap Searches 2022-05-17, 17:02
Replies: 47
Views: 6,951
Posted By mart_r
CSGmax for p<=1014: k gap CSG_max p ...

CSGmax for p<=1014:
k gap CSG_max p
1 766 0.81776202 19581334192423
2 900 0.89182288 21185697626083
3 986 0.92092951 21185697625997
4 1134 0.93874248 ...
Forum: Lounge 2022-05-17, 16:48
Replies: 1,689
Views: 191,903
Posted By mart_r
Been following the news about Covid in NK quite...

Been following the news about Covid in NK quite closely. Since the first official case reported Thursday last week, it seems to spread like crazy.
I'm suspecting that it's been there for quite a...
Forum: Lounge 2022-05-07, 16:20
Replies: 1,203
Views: 136,907
Posted By mart_r
RudeBasic V1.0 (code sample): 20 IF X<>0 THEN...

RudeBasic V1.0 (code sample):
20 IF X<>0 THEN Z=Y/X OR ELSE!!
Forum: Prime Gap Searches 2022-05-01, 14:56
Replies: 47
Views: 6,951
Posted By mart_r
Very good! That's the sort of analysis I was...

Very good! That's the sort of analysis I was looking for.
Do you have a program for these gap combinations?
Forum: Prime Gap Searches 2022-04-26, 09:18
Replies: 47
Views: 6,951
Posted By mart_r
Me too :smile: At first sight, 37 should occur...

Me too :smile:
At first sight, 37 should occur more often than 29 because the two gaps preceding 37 are {2, 6} instead of {4, 6} for 29. If however we take three gaps before the prime into account,...
Forum: Prime Gap Searches 2022-04-23, 15:59
Replies: 47
Views: 6,951
Posted By mart_r
That's what. You know, even though I don't get...

That's what. You know, even though I don't get many replies, it helps that I share my ideas here as it puts more pressure on me to think things through more thoroughly (try saying that five times...
Forum: Prime Gap Searches 2022-04-22, 17:11
Replies: 47
Views: 6,951
Posted By mart_r
What do you get if you multiply six by nine?

9439 beats 283 at around x=740000.
9439 does not appear to beat 199.
113173 may be the subsequent local maximum (beating 24109 for some x < 1.2e6). A lot more ok and a lot higher bound x would need...
Forum: Prime Gap Searches 2022-04-21, 17:04
Replies: 109
Views: 31,077
Posted By mart_r
OK, like I said I'll start testing...

OK, like I said I'll start testing 29*479909#/19#+x with -3531714 < x <= -2000000.
I won't test those -23995430 <= x < -3531714, that would take way too long :wink:
Forum: Prime Gap Searches 2022-04-21, 16:47
Replies: 138
Views: 36,292
Posted By mart_r
I'm still puzzled by how those values aM evolve....

I'm still puzzled by how those values aM evolve. They are decreasing as p gets larger, but I can't for the love of Euclid tell at what rate in the long run, let alone whether they converge or...
Forum: Prime Gap Searches 2022-04-20, 20:09
Replies: 109
Views: 31,077
Posted By mart_r
The WR gaps so far have all been fully checked,...

The WR gaps so far have all been fully checked, consequently this gap should also be fully checked IMHO.
My pocket calculator says for 36375 tests it would take me about 82 days for a full check on...
Forum: Prime Gap Searches 2022-04-19, 16:35
Replies: 109
Views: 31,077
Posted By mart_r
I could donate some cycles for PRPing (four...

I could donate some cycles for PRPing (four OpenPFGW instances, each can check one number in about 13 minutes, ballpark).
Provided that someone else can do the sieving part. Or is a list of divisors...
Forum: Prime Gap Searches 2022-04-13, 20:36
Replies: 138
Views: 36,292
Posted By mart_r
Never mind, I concocted something which I now...

Never mind, I concocted something which I now believe to be correct:
The sum [$]s(g)[/$] should be asymptotic to [$]\frac{g-1}{2c_2}-\frac{\log g}{4c_2}-\frac{5c_2}{21}[/$]

As a by-product, a...
Forum: Prime Gap Searches 2022-04-13, 20:26
Replies: 47
Views: 6,951
Posted By mart_r
p=5659 is not a good candidate for a record...

p=5659 is not a good candidate for a record number of maximal gaps after p, as you can see in the attached graph. The graph shows pn vs. on(x) at x=500000. Points further to the right have a higher...
Forum: Other Mathematical Topics 2022-04-07, 15:23
Replies: 9
Views: 3,260
Posted By mart_r
That's correct, I was considering this as well....

That's correct, I was considering this as well. And the more I think about it, the less it makes sense to find an average value of this kind.
So I rather retract my earlier statements about said...
Forum: Other Mathematical Topics 2022-04-05, 19:23
Replies: 9
Views: 3,260
Posted By mart_r
Correction: c ~ 2.14, and R(x) - also...

Correction: c ~ 2.14, and R(x) - also Li(x)-[$]\sqrt{x}[/$]/log(x) - should be ~ 8.5 times closer to [$]\pi[/$](x) by logarithmic average.
That is, until I find the next mistake in my...
Forum: Other Mathematical Topics 2022-03-28, 17:39
Replies: 9
Views: 3,260
Posted By mart_r
I think I got it now. The paper arXiv: 1407.1914...

I think I got it now. The paper arXiv: 1407.1914 "On the first sign change of [$]\theta[/$](x)-x" by Platt and Trudgian was in the scope of my knowledge, but it was not until recently I found the...
Forum: Prime Gap Searches 2022-03-25, 22:47
Replies: 138
Views: 36,292
Posted By mart_r
I have found a truly marvellous correlation. ...

I have found a truly marvellous correlation.

Let me try to explain:
The "gapfactor" - I'm trying to think of a better name, stay tuned - f(g) is defined for even g as
[$]f(g) = \prod_r...
Forum: Prime Gap Searches 2022-03-21, 22:08
Replies: 47
Views: 6,951
Posted By mart_r
You're right. For small x, 1327 and some of the...

You're right. For small x, 1327 and some of the previous primes should occur quite often as primes preceding maximal gaps. For x >= 8, 1321 occurs more often than 1327, and for x >= 10, 1303 or 1307...
Forum: Prime Gap Searches 2022-03-16, 22:06
Replies: 47
Views: 6,951
Posted By mart_r
These are the current record CSG for each k @ p...

These are the current record CSG for each k @ p <= 3.9*1013:
k gap CSG p
1 766 0.8177620175 19581334192423
2 900 0.8918228764 21185697626083
3 986 0.9209295055 ...
Forum: And now for something completely different 2022-03-16, 21:30
Replies: 22
Views: 1,330
Posted By mart_r
Very nice gigantic GRU twins! :bow: And...

Very nice gigantic GRU twins! :bow:


And there are p for which (b^p-1)/(b-1) are more prime-rich than others. Depends on how much primes of the form 2kp+1 exist, especially for small k. Good...
Forum: And now for something completely different 2022-03-12, 22:47
Replies: 22
Views: 1,330
Posted By mart_r
@ Batalov: for a moment you made me believe that...

@ Batalov: for a moment you made me believe that there are no generalized repunit primes (bp-1)/(b-1) that are members of twin primes for p > 2, but then I saw your restrictions on p...

A Pari...
Forum: And now for something completely different 2022-03-10, 21:59
Replies: 22
Views: 1,330
Posted By mart_r
It appears that this is true for 11 < p < 38000. ...

It appears that this is true for 11 < p < 38000.
There are none listed on the Lifchitz PRP page either. (Even if we relax the condition that the exponent be prime, only (10^20016-1)/9+2 is listed...
Forum: Prime Gap Searches 2022-03-10, 21:16
Replies: 47
Views: 6,951
Posted By mart_r
Herr Ober, Zahlen bitte!

Data for maximal gaps for p < 3*1013 and k <= 109 is now publicly available! Rejoice!
I'm probably taking this up to p = 1014. Well, unless anyone wants to join in.


Since the primes at the...
Forum: Other Mathematical Topics 2022-03-10, 20:20
Replies: 9
Views: 3,260
Posted By mart_r
OK thanks! This calculation doesn't have top...

OK thanks! This calculation doesn't have top priority at the moment, so it will probably take a while until I get results worth mentioning.
My favorite programming language would be the one I'm most...
Showing results 1 to 25 of 743

 
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